Neural LoFi models deep learning as layer-wise spectral filtering that selects maximal low-degree correlations, yielding a tractable surrogate for hierarchical representation learning beyond the lazy regime.
arXiv preprint arXiv:2602.10867 , year=
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Two steps of gradient descent on first-layer weights in linear-width two-layer networks produce a spiked random matrix with floor(alpha2/(1/2-alpha1)) outliers, each a learned direction, and batch reuse allows capturing directions with information exponent exceeding one.
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Deep Learning as Neural Low-Degree Filtering: A Spectral Theory of Hierarchical Feature Learning
Neural LoFi models deep learning as layer-wise spectral filtering that selects maximal low-degree correlations, yielding a tractable surrogate for hierarchical representation learning beyond the lazy regime.
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Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent
Two steps of gradient descent on first-layer weights in linear-width two-layer networks produce a spiked random matrix with floor(alpha2/(1/2-alpha1)) outliers, each a learned direction, and batch reuse allows capturing directions with information exponent exceeding one.